We discuss the electrostatic contribution to the elastic moduli of a cell or artificial membrane placed in an electrolyte and driven by a DC electric field. The field drives ion currents across the membrane, through specific channels, pumps or natural pores. In steady state, charges accumulate in the Debye layers close to the membrane, modifying the membrane elastic moduli. We first study a model of a membrane of zero thickness, later generalizing this treatment to allow for a finite thickness and finite dielectric constant. Our results clarify and extend the results presented in [D. Lacoste, M. Cosentino Lagomarsino, and J. F. Joanny, Europhys. Lett., {\bf 77}, 18006 (2007)], by providing a physical explanation for a destabilizing term proportional to $\kps^3$ in the fluctuation spectrum, which we relate to a nonlinear ($E^2$) electro-kinetic effect called induced-charge electro-osmosis (ICEO). Recent studies of ICEO have focused on electrodes and polarizable particles, where an applied bulk field is perturbed by capacitive charging of the double layer and drives flow along the field axis toward surface protrusions; in contrast, we predict "reverse" ICEO flows around driven membranes, due to curvature-induced tangential fields within a non-equilibrium double layer, which hydrodynamically enhance protrusions. We also consider the effect of incorporating the dynamics of a spatially dependent concentration field for the ion channels.
Liquid transport through nanopore is central into many applications, from water purification to biosensing or energy harvesting. Ultimately thin nanopores are of major interest in these applications to increase driving potential and reduce as much as possible dissipation sources. We investigate here the efficiency of the electrical power generation through an ultrathin nanoporous membrane by means of streaming current (electrical current induced by ionic flow in the vicinity of the liquid/solid interface) or electroosmosis (flow rate induced by an electrical potential). Upscaling from one uniq…
The theory of electrokinetic ion transport in cylindrical channels of a fixed surface charge density is revisited. Attention is focused on impact of the hydrophobic slippage and mobility of adsorbed surface charges. We formulate generalised Onsager relations for a cylinder of an arbitrary radius and then derive exact expressions for the mean electro-osmotic mobility and conductivity. To employ these expressions we perform additional electrostatic calculations, with the special focus on the non-linear electrostatic effects. Our theory provides a simple explanation of a giant enhancement of the …
A new computational method is presented for study suspensions of charged soft particles undergoing fluctuating hydrodynamic and electrostatic interactions. The proposed model is appropriate for polymers, proteins and porous particles embedded in a continuum electrolyte. A self-consistent Langevin description of the particles is adopted in which hydrodynamic and electrostatic interactions are included through a Green's function formalism. An Ewald-like split is adopted in order to satisfy arbitrary boundary conditions for the Stokeslet and Poisson Green functions, thereby providing a formalism …
A new lattice method is presented in order to efficiently solve the electrokinetic equations, which describe the structure and dynamics of the charge cloud and the flow field surrounding a single charged colloidal sphere, or a fixed array of such objects. We focus on calculating the electrophoretic mobility in the limit of small driving field, and systematically linearise the equations with respect to the latter. This gives rise to several subproblems, each of which is solved by a specialised numerical algorithm. For the total problem we combine these solvers in an iterative procedure. Applyin…
We study ionic and mass transport in a liquid crystalline fluid film in its nematic phase under an applied electrostatic field. Both analytic and numerical solutions are given for some prototypical configurations of interest in electrokinetics: Thin films with spatially nonuniform nematic director that are either periodic or comprise a set of isolated disclinations. We present a quantitative description of the mechanisms inducing spatial charge separation in the nematic, and of the structure and magnitude of the resulting flows. The fundamental solutions for the charge distribution and flow ve…
We probe the electrostatic cost associated with the approach phase of DNA translocation events. Within an analytical theory at the Debye-Huckel level, we calculate the electrostatic free energy of a rigid DNA molecule interacting with a dielectric membrane. For carbon or silicon based low permittivity neutral membranes, the DNA molecule experiences a repulsive energy barrier between 10 kBT and 100 kBT. In the case of engineered membranes with high dielectric permittivity, the membrane surface attracts the DNA with an energy of the same magnitude. Both the repulsive and attractive interactions …
Ionic and molecular selectivity is considered unique for the nanoscale and not realizable in microfluidics. This is due to the scale-matching problem -- a difficulty to match the dimensions of ions and electrostatic potential screening lengths with the micron-sized confinements. Here, we demonstrate a microscale realization of the ionic transport processes closely resembling those specific to ionic channels or in nanofluidic junctions, including selectivity, guidance through complex geometries and flow focusing. As a model system, we explore electrokinetic spherical Janus micromotors moving ov…
We investigate the effect on biomembrane mechanical properties due to the presence an external potential for a non-conductive non-compressible membrane surrounded by different electrolytes. By solving the Debye-Huckel and Laplace equations for the electrostatic potential and using the relevant stress-tensor we find: in (1.) the small screening length limit, where the Debye screening length is smaller than the distance between the electrodes, the screening certifies that all electrostatic interactions are short-range and the major effect of the applied potential is to decrease the membrane tens…
We study the non-equilibrium dynamics of lipid membranes with proteins that actively pump ions across the membrane. We find that the activity leads to a fluctuating force distribution due to electrostatic interactions arising from variation in dielectric constant across the membrane. By applying a multipole expansion we find effects on both the tension and bending rigidity dominated parts of the membranes fluctuation spectrum. We discuss how our model compares with previous studies of force-multipole models.
We consider the influence of electrostatic forces on driven translocation dynamics of a flexible polyelectrolyte being pulled through a nanopore by an external force on the head monomer. To this end, we augment the iso-flux tension propagation (IFTP) theory with electrostatics for a negatively charged biopolymer pulled through a nanopore embedded in a similarly charged anionic membrane. We show that for the realistic case such as a single-stranded DNA, the translocation dynamics at low salt where screening is weak and at finite negative membrane charge is unexpectedly accelerated despite the l…
Bending rigidity of a charged membrane or a charged polyelectrolyte screened by monovalent counterions is known to be enhanced by electrostatic effects. We show that in the case of screening by multivalent counterions the electrostatic effects reduce the bending rigidity. This inversion of the sign of the electrostatic contribution is related to the formation of two-dimensional strongly correlated liquids (SCL) of counterions at the charged surface due to strong lateral repulsion between them. When a membrane or a polyelectrolyte is bent, SCL is compressed on one side and stretched on the othe…
We consider an osmotic equilibrium between bulk solutions of polyelectrolyte bounded by semipermeable membranes and separated by a thin film of salt-free liquid. Although the membranes are neutral, the counter-ions of the polyelectrolyte molecules permeate into the gap and lead to a steric charge separation. This gives rise to a distance-dependent membrane potential, which translates into a repulsive electrostatic disjoining pressure. From the solution of the non-linear Poisson-Boltzmann equation we obtain the distribution of the potential and of ions. We then derive an explicit formula for th…
We characterize the role of charge correlations in the adsorption of a short, rod-like anionic polyelectrolyte onto a similarly charged membrane. Our theory reveals two different mechanisms driving the like-charge polyelectrolyte-membrane complexation: in weakly charged membranes, repulsive polyelectrolyte-membrane interactions lead to the interfacial depletion and a parallel orientation of the polyelectrolyte with respect to the membrane; while in the intermediate membrane charge regime, the interfacial counterion excess gives rise to an attractive "salt-induced" image force. This furthermore…
For many biotechnological applications it would be useful to better understand the effects produced by electric fields on lipid membranes. This review discusses several aspects of the electrostatic properties of a planar lipid membrane with its surrounding electrolyte in a normal DC or AC electric field. In the planar geometry, the analysis of electrokinetic equations can be carried out quite far, allowing to characterize analytically the steady state and the dynamics of the charge accumulation in the Debye layers, which results from the application of the electric field. For a conductive memb…
We characterize the role of electrostatic fluctuations on the charge selectivity of cylindrical nanopores confining electrolyte mixtures. To this end, we develop an extended one-loop theory that can account for correlation effects induced by the surface charge, nanoconfinement of the electrolyte, and interfacial polarization charges associated with the low permittivity membrane. We validate the quantitative accuracy of the theory by comparisons with previously obtained Monte-Carlo simulation data from the literature, and scrutinize in detail the underlying forces driving the ionic selectivity …
In this paper we study the electrostatic interaction of a heterogeneously charged wall with a neutral semipermeable membrane. The wall consists of periodic stripes, where the charge density varies in one direction. The membrane is in a contact with a bulk reservoir of an electrolyte solution and separated from the wall by a thin film of salt-free liquid. One type of ions (small counterions) permeates into the gap and gives rise to a distance-dependent membrane potential, which translates into a repulsive electrostatic disjoining pressure due to an overlap of counterion clouds in the gap. To qu…
We consider the electrostatic interaction between two rigid membranes, with different surface charge densities of opposite sign, across an aqueous solution without added salt. Exact solutions to the nonlinear Poisson-Boltzmann equation are obtained and their physical meaning discussed. We also calculate the electrostatic contribution to the free energy and discuss the renormalization of the area per head group of the charged lipids arising from the Coulomb interaction.
We develop an analytical theory that accounts for the image and surface charge interactions between a charged dielectric membrane and a DNA molecule translocating through the membrane. Translocation events through neutral carbon-based membranes are driven by a competition between the repulsive DNA-image-charge interactions and the attractive coupling between the DNA segments on the trans and the cis sides of the membrane. The latter effect is induced by the reduction of the coupling by the dielectric membrane. In strong salt solutions where the repulsive image-charge effects dominate the attra…
The electrostatic Schwinger-Dyson equations are derived and solved for an electrolyte mixture composed of mono- and multivalent ions confined to a negatively charged nanoslit. The closure of these equations is based on an asymmetric treatment of the ionic species with respect to their electrostatic coupling strength; the weakly coupled monovalent ions are treated within a gaussian approximation while the multivalent counterions of high coupling strength are incorporated with a strong-coupling approach. The resulting self-consistent formalism includes explicitly the interactions of the multival…
In ion-exchange membrane processes, ions and water flow under the influence of gradients in hydrostatic pressure, ion chemical potential, and electrical potential (voltage), leading to solvent flow, ionic fluxes and ionic current. At the outer surfaces of the membranes, electrical double layers (EDLs) are formed (Donnan layers). When a current flows through the membrane, we argue that besides Joule heating in the bulk of the membrane and in the electrolyte outside the membrane, there is also electrostatic heating and cooling in the EDLs. In addition, when fluid flows through a charged membrane…
We present theoretical work in which the degree of electrostatic coupling across a charged lipid bilayer in aqueous solution is analyzed on the basis of nonlinear Poisson-Boltzmann theory. In particular, we consider the electrostatic interaction of a single, large macroion with the two apposed leaflets of an oppositely charged lipid bilayer where the macroion is allowed to optimize its distance to the membrane. Three regimes are identified: a weak and a high macroion charge regime, separated by a regime of close macroion-membrane contact for intermediate charge densities. The corresponding fre…
We use a coarse-grained molecular dynamics simulation to investigate the interaction between neutral or charged nanoparticles (NPs) and a vesicle consisting of neutral and negatively charged lipids. We focus on the interaction strengths of hydrophilic and hydrophobic attraction and electrostatic interactions between a lipid molecule and an NP. A neutral NP passes through the lipid membrane when the hydrophobic interaction is sufficiently strong. As the valence of the positively charged NP increases, the membrane permeation speed of the NP is increased compared with the neutral NP and charged l…
The effect of AC electric fields on the elasticity of supported lipid bilayers has been investigated at the microscopic level using grazing incidence synchrotron x-ray scattering. A strong decrease in the membrane tension up to 1mN/m and a dramatic increase of its effective rigidity up to 300kBT are observed for local electric potentials seen by the membrane < 1V. The experimental results were analyzed using detailed electrokinetic modeling and non-linear Poisson-Boltzmann theory. Based on a modeling of the electromagnetic stress which provides an accurate description of bilayer separation vs …
Significant temperature effects on the electrokinetic transport in a nanochannel with a slab geometry are demonstrated using a molecular dynamics (MD) model. A system consisting of Na+ and Cl- ions dissolved in water and confined between fixed crystalline silicon walls with negatively charged inner surfaces in an external electric field was investigated. Lennard-Jones (LJ) force fields and Coulomb electrostatic interactions with Simple Point Charge Extended (SPC/E) model were used to represent the interactions between ions, water molecules, and channel wall atoms. Dependence of the flow of wat…
The behavior of a non-conductive quasi-planar lipid membrane in an electrolyte and in a static (DC) electric field is investigated theoretically in the nonlinear (Poisson-Boltzmann) regime. Electrostatic effects due to charges in the membrane lipids and in the double layers lead to corrections to the membrane elastic moduli which are analyzed here. We show that, especially in the low salt limit, i) the electrostatic contribution to the membrane's surface tension due to the Debye layers crosses over from a quadratic behavior in the externally applied voltage to a linear voltage regime. ii) the …
A model of a finite cylindrical ion channel through a phospholipid membrane of width $L$ separating two electrolyte reservoirs is studied. Analytical solution of the Poisson equation is obtained for an arbitrary distribution of ions inside the trans-membrane pore. The solution is asymptotically exact in the limit of large ionic strength of electrolyte on the two sides of membrane. However, even for physiological concentrations of electrolyte, the electrostatic barrier sizes found using the theory are in excellent agreement with the numerical solution of the Poisson equation. The analytical sol…
We probe the electrostatic mechanism driving adsorption of polyelectrolytes onto like-charged membranes upon the addition of tri- and tetravalent counterions to a bathing monovalent salt solution. We develop a one-loop-dressed strong coupling theory that treats the monovalent salt at the electrostatic one-loop level and the multivalent counterions within a strong-coupling approach. It is shown that the adhesive force of the multivalent counterions mediating the like-charge adsorption arises from their strong condensation at the charged membrane. The resulting interfacial counterion excess loca…
We propose a very simple but realistic enough model which allows to include a large number of molecules in molecular dynamics MD simulations of these bilayers, but nevertheless taking into account molecular charge distributions, flexible amphiphilic molecules and a reliable model of water. All these parameters are essential in a nanoscopic scale study of intermolecular and long range electrostatic interactions. This model was previously used by us to simulate a Newton black film and in this paper we extend our investigation to bilayers of the biological membrane type. The electrostatic interac…
This paper considers the effect of electrostatics on the stability of a charged membrane. We show that at low ionic strength and high surface charge density, repulsion between charges on the membrane renders it unstable to the formation of holes. A free straight edge is unstable to modulations with wavelength longer than the Debye screening length. Hence at low ionic strength, membranes will disintegrate into vesicles. We use these results to interpret stable holes in red blood cell ghosts (Steck et. al., Science 168:255(1970)).
Sensitive sequencing of biopolymers by nanopore-based translocation techniques requires extension of the time spent by the molecule in the pore. We develop an electrostatic theory of polymer translocation to show that the translocation time can be extended via the dielectric trapping of the polymer. In dilute salt conditions, the dielectric contrast between the low permittivity membrane and large permittivity solvent gives rise to attractive interactions between the cis and trans portions of the polymer. This self-attraction acts as a dielectric trap that can enhance the translocation time by …
Motivated by biological membrane-containing organelles in plants and photosynthetic bacteria, we study charge regulation in a model membrane stack. Considering (de)protonation as the simplest mechanism of charge equilibration between the membranes and with the bathing environment, we uncover a symmetry-broken charge state in the stack with a quasiperiodic effective charge sequence. In the case of a monovalent bathing salt solution our model predicts complex, inhomogeneous charge equilibria depending on the strength of the (de)protonation reaction, salt concentration, intermembrane separation, …
The electrostatic screening of charge in one-dimensional confinement leads to long-range breakdown in electroneutrality within a nanopore. Through a series of continuum simulations, we demonstrate the principles of electroneutrality breakdown for electrolytes in one dimensional confinement. We show how interacting pores in a membrane can counteract the phenomenon of electroneutrality breakdown, eventually returning to electroneutrality. Emphasis is placed on applying simplifying formulas to reduce the multidimensional partial differential equations into a single ordinary differential equation …
Manipulating the shape of nanoscale objects in a controllable fashion is at the heart of designing materials that act as building blocks for self-assembly or serve as targeted drug delivery carriers. Inducing shape deformations by controlling external parameters is also an important way of designing biomimetic membranes. In this paper, we demonstrate that electrostatics can be used as a tool to manipulate the shape of soft, closed membranes by tuning environmental conditions such as the electrolyte concentration in the medium. Using a molecular dynamics-based simulated annealing procedure, we …
We consider two charged semipermeable membranes, which bound bulk electrolyte solutions and are separated by a thin film of salt-free liquid. Small counter-ions permeate into the gap, which leads to a steric charge separation in the system. To quantify the problem, we define an effective surface charge density of imaginary impermeable surface, which mimics an actual semipermeable membrane and greatly simplify analysis. The effective charge depends on separation, generally differ from the real one, and could even be of the opposite sign. From the exact and asymptotic solutions of the nonlinear …
Translocation properties of ionic channels are investigated, on the basis of classical electrostatics, with an emphasis on asymptotic formulas for the potential and field associated with a point charge in the channel. Due to image charges in the membrane, we show that ions in an infinite length channel interact via a one-dimensional (1D) Coulomb potential. The corresponding electrostatic barrier $Σ$ is characterized by a "geometric mean" screening $Σ\propto e^2 / \sqrt{ε_w ε_m}R$ ($R$ being the radius of the pore, and $ε_m \approx 2$ and $ε_w \approx 80$ the room temperature dielectric constan…
We study the strong-coupling (SC) interaction between two like-charged membranes of finite thickness embedded in a medium of higher dielectric constant. A generalized SC theory is applied along with extensive Monte-Carlo simulations to study the image charge effects induced by multiple dielectric discontinuities in this system. These effects lead to strong counterion crowding in the central region of the inter-surface space upon increasing the solvent/membrane dielectric mismatch and change the membrane interactions from attractive to repulsive at small separations. These features agree quanti…
We predict the nature (attractive or repulsive) and range (exponentially screened or long-range power law) of the electrostatic interactions of oppositely charged and planar plates as a function of the salt concentration and surface charge densities (whose absolute magnitudes are not necessarily equal). An analytical expression for the crossover between attractive and repulsive pressure is obtained as a function of the salt concentration. This condition reduces to the high-salt limit of Parsegian and Gingell where the interaction is exponentially screened and to the zero salt limit of Lau and …
We develop a model of interacting zwitterionic membranes with rotating surface dipoles immersed in a monovalent salt, and implement it in a field theoretic formalism. In the mean-field regime of monovalent salt, the electrostatic forces between the membranes are characterized by a non-uniform trend: at large membrane separations, the interfacial dipoles on the opposing sides behave as like-charge cations and give rise to repulsive membrane interactions; at short membrane separations, the anionic field induced by the dipolar phosphate groups sets the behavior in the intermembrane region. The at…
Lipid rafts are hypothesized to facilitate protein interaction, tension regulation, and trafficking in biological membranes, but the mechanisms responsible for their formation and maintenance are not clear. Insights into many other condensed matter phenomena have come from colloidal systems, whose micron-scale particles mimic basic properties of atoms and molecules but permit dynamic visualization with single-particle resolution. Recently, experiments showed that bidisperse mixtures of filamentous viruses can self-assemble into colloidal monolayers with thermodynamically stable rafts exhibitin…
We formulate a theory of electrostatic interactions in lipid bilayer membranes where both monolayer leaflets contain dissociable moieties that are subject to charge regulation. We specifically investigate the coupling between membrane curvature and charge regulation of a lipid bilayer vesicle using both the linear Debye-Hückel (DH) and the non-linear Poisson-Boltzmann (PB) theory. We find that charge regulation of an otherwise symmetric bilayer membrane can induce charge symmetry breaking, non-linear flexoelectricity and anomalous curvature dependence of free energy. The pH effects investigate…
Polymer translocation experiments typically involve anionic polyelectrolytes such as DNA molecules driven through negatively charged nanopores. Quantitative modelling of polymer capture to the nanopore followed by translocation therefore necessitates the consideration of the electrostatic barrier resulting from like-charge polymer-pore interactions. To this end, in this work we couple mean-field level electrohydrodynamic equations with the Smoluchowski formalism to characterize the interplay between the electrostatic barrier, the electrophoretic drift, and the electro-osmotic liquid flow. In p…
Processes based on electrostatic projection are used extensively in industry, e.g. for mineral separations, electrophotography or manufacturing of coated abrasives, such as sandpaper. Despite decades of engineering practice, there are still unanswered questions. In this paper, we present a comprehensive experimental study of projection process of more than 1500 individual spherical alumina particles with a nominal size of 500 $μ$m, captured by high-speed video imaging and digital image analysis. Based on flight trajectories of approximately 1100 projected particles, we determined the acquired …
Understanding interactions between membranes requires measurements on well-controlled systems close to natural conditions, in which fluctuations play an important role. We have determined, by grazing incidence X-ray scattering, the interaction potential between two lipid bilayers, one adsorbed on a solid surface and the other floating close by. We find that interactions in this highly hydrated model system are two orders of magnitude softer than in previously reported work on multilayer stacks. This is attributed to the weak electrostatic repulsion due to the small fraction of ionized lipids i…
We study the contribution of polyelectrolytes in solution to the bending moduli of charged membranes. Using the Helfrich free energy, and within the mean-field theory, we calculate the dependence of the bending moduli on the electrostatics and short-range interactions between the membrane and the polyelectrolyte chains. The most significant effect is seen for strong short-range interactions and low amounts of added salt where a substantial increase in the bending moduli of order $1 k_BT$ is obtained. From short-range repulsive membranes, the polyelectrolyte contribution to the bending moduli i…
We construct a mean-field formulation of the thermodynamics of ion solvation in immiscible polar binary mixtures. Assuming an equilibrium planar interface separating two semi-infinite regions of different constant dielectric medium, we study the electrostatic phenomenon of differential adsorption of ions at the interface. Using general thermodynamic considerations, we construct the mean-field $Ω$-potential and demonstrate the spontaneous formation of an electric double-layer around the interface necessarily follow. In our framework, we can also relate both the bulk ion densities in the two pha…
We have studied the electrostatic screening effect of NaCl solutions on the interactions between anionic lipid bilayers in the fluid lamellar phase using a Poisson-Boltzmann based mean-field approach with constant charge and constant potential limiting charge regulation boundary conditions. The full DLVO potential, including the electrostatic, hydration and van der Waals interactions, was coupled to thermal bending fluctuations of the membranes via a variational Gaussian Ansatz. This allowed us to analyze the coupling between the osmotic pressure and the fluctuation amplitudes and compare them…
We use coarse-grained Monte Carlo simulations to study the elastic properties of charged membranes in solutions of monovalent and pentavalent counterions. The simulation results of the two cases reveal trends opposite to each other. The bending rigidity and projected area increase with the membrane charge density for monovalent counterions, while they decrease for the pentavalent ions. These observations can be related to the counterion screening of the lipid charges. While the monovalent counterions only weakly screen the Coulomb interactions, which implies a repulsive Coulomb system, the mul…
Ionic microgels are soft colloidal particles, composed of crosslinked polymer networks, that ionize and swell when dispersed in a good solvent. Swelling of these permeable, compressible particles involves a balance of electrostatic, elastic, and mixing contributions to the single-particle osmotic pressure. The electrostatic contribution depends on the distributions of mobile counterions and coions and of fixed charge on the polymers. Within the cell model, we employ two complementary methods to derive the electrostatic osmotic pressure of ionic microgels. In Poisson-Boltzmann (PB) theory, we m…
Cationic lipid membranes are known to form compact complexes with DNA and to be effective as gene delivery agents both in vitro and in vivo. Here we employ molecular dynamics simulations for a detailed atomistic study of lipid bilayers consisting of a mixture of cationic dimyristoyltrimethylammonium propane (DMTAP) and zwitterionic dimyristoylphosphatidylcholine (DMPC). Our main objective is to examine how the composition of the bilayers affects their structural and electrostatic properties in the liquid-crystalline phase. By varying the mole fraction of DMTAP, we have found that the area per …
